Peano's Parlour

This site is dedicated to open problems in nonstandard models of Paeno Arithmetic and related theory. As in most areas, we do not suffer from a shortage of open problems. The problems are arranged by category. Here is the list of categories.

1. Cuts in models of PA and independence results

[[2. Recursively saturated, resplendent models, and saturated models. ]] 3. Automorphisms and automorphism groups.

4. Standard systems and the Scott set problem.

5. Lattices of elementary substructures.

6. Uncounrtable models with interesting second-order properies.

7. Nonstandard satisfaction classes.

8. Model theory of strong fragments of arithmetic.

9. Model theory of weak fragments of arithmetic.

10. Model theoretic methods in proof theory.